Problem: Solve for $x$ and $y$ using substitution. ${6x-6y = 6}$ ${y = 5x-9}$
Answer: Since $y$ has already been solved for, substitute $5x-9$ for $y$ in the first equation. ${6x - 6}{(5x-9)}{= 6}$ Simplify and solve for $x$ $6x-30x + 54 = 6$ $-24x+54 = 6$ $-24x+54{-54} = 6{-54}$ $-24x = -48$ $\dfrac{-24x}{{-24}} = \dfrac{-48}{{-24}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {y = 5x-9}\thinspace$ to find $y$ ${y = 5}{(2)}{ - 9}$ $y = 10 - 9$ $y = 1$ You can also plug ${x = 2}$ into $\thinspace {6x-6y = 6}\thinspace$ and get the same answer for $y$ : ${6}{(2)}{ - 6y = 6}$ ${y = 1}$